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Search: id:A131962
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| A131962 |
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Expansion of q^(-7/24) * eta(q^2)^2 * eta(q^8) * eta(q^12)^2/( eta(q) * eta(q^4) * eta(q^24)) in powers of q. |
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6
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| 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 1, 0, 0, 1, 1, 1, 2, 0, 2, 0, 1, 1, 0, 2, 2, 1, 1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 2, 3, 0, 1, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 0, 3, 1, 1, 2, 0, 0, 1, 2, 0, 0, 1, 1, 2, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 1, 0, 2, 1, 0, 0, 0, 2, 1
(list; graph; listen)
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OFFSET
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0,11
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FORMULA
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Expansion of psi(q)* phi(-q^12)/ chi(-q^4) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
Euler transform of period 24 sequence [ 1, -1, 1, 0, 1, -1, 1, -1, 1, -1, 1, -2, 1, -1, 1, -1, 1, -1, 1, 0, 1, -1, 1, -2, ...].
a(25n+7)= a(n). a(25n+2)= a(25n+12)= a(25n+17)= a(25n+22)= 0.
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PROGRAM
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(PARI) {a(n)= if(n<0, 0, n=24*n+7; sumdiv(n, d, kronecker( -12, d)*(n/d %2))/2)}
(PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( eta(x^2+A)^2* eta(x^8+A)* eta(x^12+A)^2/ eta(x+A)/ eta(x^4+A)/ eta(x^24+A), n))}
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CROSSREFS
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Cf. A123484(24n+7)= 2*a(n).
Sequence in context: A106347 A124300 A027186 this_sequence A072575 A025872 A112344
Adjacent sequences: A131959 A131960 A131961 this_sequence A131963 A131964 A131965
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 02 2007
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